The German international captain, who has endured a lean season, scored a 51st-minute winner, beating the goalkeeper Uwe Kamps from close range from a pass by Mario Basler, to please most of the crowd of 63,000.
Bayern now go into the winter break at the top of the table for the 10th time since they entered the Bundesliga in 1965, ending the autumn campaign with 36 points, two more than the champions, Borussia Dortmund, who beat Cologne 3-1.
Bayern's coach, Giovanni Trapattoni, said: "Being autumn champion is not enough, the result comes at the end of May. I am happy but the team has to improve. Despite having many injuries in the autumn season, we are still standing in first place."
After the match Monchengladbach, who lie second from bottom, dismissed their coach, Bernd Krauss. Eintracht Frankfurt, who are struggling in the Bundesliga Second Division and are in danger of relegation the regional leagues, also sacked their coach: the former Manchester City defender Dragoslav Stepanovic.
In Italy, Milan banished some of the memories of Wednesday's Champions' League humiliation by Rosenborg Trondheim with a 2-1 home win over Udinese. Arrigo Sacchi, picking a Milan team in Serie A for the first time since May 1991, dropped the goalkeeper Sebastiano Rossi, whose errors cost his side dear against the Norwegians.
Dejan Savicevic headed Milan into a second-half lead soon after coming off the bench. Giovanni Stroppa, a former Milan player, soon equalised but Stefano Eranio snatched the winner. Another substitute, Jesper Blomqvist, made a promising second-half debut for Milan.
Milan are four points behind Vicenza, who are top of Serie A on goal difference, and Juventus. Vicenza were held 1-1 at home by third-placed Internazionale, who levelled with Youri Djorkaeff's second-half penalty, while Juventus won 1-0 at Sampdoria thanks to Ciro Ferrara's first-half goal
Ajax had another bad day in the Dutch League when they were held 1-1 at AZ Alkmaar. Arno Splinter's deflected shot put them ahead after 11 minutes and then Alkmaar's Danny Hesp was sent off for bringing down Nordin Wooter after 30 minutes, but Krzystof Bociek headed a 55th-minute equaliser. Ajax languish in sixth place, 15 points behind the leaders, PSV Eindhoven, who thrashed Volendam 6-0 on Saturday.Reuse content